*4.12. Oxygen Permeability*

An oxygen permeation analyzer (8001, Systech Illinois Instruments Co., Johnsburg, IL, USA) was used to measure the oxygen transmission rate (OTR) through the tested films. Following the ASTM D 3985 method the experimental conditions were regulated at 23 ◦C and 0% RH and the measured OTR values were expressed in cc O2/m2/day.

Gas permeability through polymers can be expressed according to the literature [63], as follows:

$$\frac{\text{J}}{\text{A}} = \text{Pe}\_{\text{gas}} \cdot \frac{\Delta \text{C}}{\Delta \text{x}} \tag{5}$$

where J/A (mol·cm−<sup>2</sup> ·s −1 ) is the specific molar rate of gas which permeates through the membrane, Pegas (cm<sup>2</sup> ·s −1 ) is the permeability coefficient of the gas, <sup>∆</sup>C (mol·cm−<sup>3</sup> STP) is the concentration gradient between the two opposite sides of the membrane, and ∆x (cm) is the membrane thickness.

Rearranging Equation (5) we can express the permeability coefficient as follows:

$$\mathrm{Pe\_{gas}} = \frac{\mathrm{J}}{\mathrm{A} \cdot \Delta \mathrm{C}} \cdot \Delta \mathrm{x} \tag{6}$$

By carrying out a dimensional analysis, the term J/(A\*∆C) (cm<sup>3</sup> STP·cm−<sup>2</sup> ·s −1 )) is equal to the OTR measurements. Thus, in our case of oxygen gas,

$$\text{Pe}\_{\text{O}\_2} = \text{OTR} \cdot \text{\Delta x} \tag{7}$$

where PeO2 (cm<sup>2</sup> ·s −1 ) is the oxygen permeability coefficient, OTR (cm<sup>3</sup> STP·cm−<sup>2</sup> ·s −1 ) is the experimentally measured by the instrument oxygen transmission rate, and ∆x (cm) is the mean film thickness.

Thus, the oxygen permeability coefficient values (PeO2) of the tested samples were calculated by multiplying the OTR values by the average film thickness which was 0.035 mm. The OTR value for each kind of film was the mean value of measurements on three different pieces.
